Gimbal Bounding Box Tracking

Problem Statement

Bounding-box tracking aligns camera orientation to maintain target centering and approximate scale regulation in image space. It is a practical visual-tracking controller when depth is partially observable.

Model and Formulation

Let (u,v) be target center and (u^*,v^*) desired image center. Error:

$$e=[u-u^{\ast },v-v^{\ast }{]}^{\mathrm{\top }}$$

PD control with smoothing:

$$u_{cmd}=K_{p}e+K_d\dot{e},e_f=\alpha e+(1-\alpha )e_f^{-}$$

Algorithm Procedure

1. Detect target bounding box each frame.
2. Compute center error and filtered derivatives.
3. Convert error to pan-tilt command increments.
4. Handle target loss with hold-and-search behavior.

Tuning and Failure Modes

• Normalised device coordinates are not angles. NDC spans the entire field of view over [-1, 1], so converting requires the FOV: θ = arctan(ndc · tan(fov/2)). Feeding NDC straight into a positional gimbal command makes the loop's real gain depend on the lens — with a 0.6 rad FOV, one unit of NDC is about 3.2 radians of apparent gain. The loop runs far past its stability limit and bounces between its rate limits, which reads as a tracking error but is a limit cycle.

• Command an angular rate and integrate it, so the gimbal's own rate limit is a limit rather than the only thing holding the loop together. Gains are then in 1/s and the closed-loop time constant is 1/k_p.

• A pan-tilt gimbal has a singularity on its own zenith. With the target passing directly underneath, bearing sweeps through π faster than any finite slew rate can follow. The resulting loss of lock is geometry, not control — put the observer beside the ground track, not above its centre. Doing so takes mean pointing error from 0.285 to 0.046 NDC.

• Large derivative gain amplifies detector jitter.

• Heavy filtering reduces noise but adds tracking lag.

• Persistent target dropout requires robust reacquisition logic.

Implementation and Execution

python -m uav_sim.simulations.sensors.gimbal_bbox_tracking

Evidence

References

• Chaumette and Hutchinson, Visual Servo Control Part II (2007)
• Szeliski, Computer Vision: Algorithms and Applications

Related Algorithms

• Gimbal Tracking
• Visual Servoing